%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 21 21:35:21 EDT 2022 % Result : Theorem 0.18s 0.40s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.11/0.33 % Computer : n018.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Sun May 29 04:43:10 EDT 2022 % 0.11/0.33 % CPUTime : % 0.18/0.40 % SZS status Theorem % 0.18/0.40 (* PROOF-FOUND *) % 0.18/0.40 (* BEGIN-PROOF *) % 0.18/0.40 % SZS output start Proof % 0.18/0.40 1. (-. (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0))) (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) ### Axiom % 0.18/0.40 2. (All X1, (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over X1 T_2) (apply X1 T_0))) (-. (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0))) ### All 1 % 0.18/0.40 3. (All A1, (All X1, (an_open_function_from_onto (the_projection_function T_0 T_1 A1) (the_product_top_space_over X1 A1) (apply X1 T_0)))) (-. (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0))) ### All 2 % 0.18/0.40 4. (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function T_0 X A1) (the_product_top_space_over X1 A1) (apply X1 T_0))))) (-. (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0))) ### All 3 % 0.18/0.40 5. (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (-. (an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0))) ### All 4 % 0.18/0.40 6. (a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) (-. (a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0))) ### Axiom % 0.18/0.40 7. (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (-. (a_locally_compact_top_space (the_product_top_space_over T_1 T_2))) ### Axiom % 0.18/0.40 8. (-. (a_locally_compact_top_space (apply T_1 T_0))) (a_locally_compact_top_space (apply T_1 T_0)) ### Axiom % 0.18/0.40 9. (((an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) /\ ((a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) /\ (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)))) => (a_locally_compact_top_space (apply T_1 T_0))) (-. (a_locally_compact_top_space (apply T_1 T_0))) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) ### DisjTree 5 6 7 8 % 0.18/0.40 10. (All B, (((an_open_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) B) /\ ((a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) B) /\ (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)))) => (a_locally_compact_top_space B))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (-. (a_locally_compact_top_space (apply T_1 T_0))) ### All 9 % 0.18/0.40 11. (All A, (All B, (((an_open_function_from_onto (the_projection_function T_0 T_1 T_2) A B) /\ ((a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B)))) (-. (a_locally_compact_top_space (apply T_1 T_0))) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) ### All 10 % 0.18/0.40 12. (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (a_continuous_function_from_onto (the_projection_function T_0 T_1 T_2) (the_product_top_space_over T_1 T_2) (apply T_1 T_0)) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (-. (a_locally_compact_top_space (apply T_1 T_0))) ### All 11 % 0.18/0.40 13. (All A1, (a_continuous_function_from_onto (the_projection_function T_0 T_1 A1) (the_product_top_space_over T_1 A1) (apply T_1 T_0))) (-. (a_locally_compact_top_space (apply T_1 T_0))) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) ### All 12 % 0.18/0.40 14. (All X, (All A1, (a_continuous_function_from_onto (the_projection_function T_0 X A1) (the_product_top_space_over X A1) (apply X T_0)))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (-. (a_locally_compact_top_space (apply T_1 T_0))) ### All 13 % 0.18/0.40 15. (All A, (All X, (All A1, (a_continuous_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X A1) (apply X A))))) (-. (a_locally_compact_top_space (apply T_1 T_0))) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) ### All 14 % 0.18/0.40 16. (-. (All A, (a_locally_compact_top_space (apply T_1 A)))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) (All A, (All X, (All A1, (a_continuous_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X A1) (apply X A))))) ### NotAllEx 15 % 0.18/0.40 17. (-. ((a_locally_compact_top_space (the_product_top_space_over T_1 T_2)) => (All A, (a_locally_compact_top_space (apply T_1 A))))) (All A, (All X, (All A1, (a_continuous_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X A1) (apply X A))))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) ### NotImply 16 % 0.18/0.40 18. (-. (All A1, ((a_locally_compact_top_space (the_product_top_space_over T_1 A1)) => (All A, (a_locally_compact_top_space (apply T_1 A)))))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (All A, (All X, (All A1, (a_continuous_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X A1) (apply X A))))) ### NotAllEx 17 % 0.18/0.40 19. (-. (All X1, (All A1, ((a_locally_compact_top_space (the_product_top_space_over X1 A1)) => (All A, (a_locally_compact_top_space (apply X1 A))))))) (All A, (All X, (All A1, (a_continuous_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X A1) (apply X A))))) (All A, (All X, (All A1, (All X1, (an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)))))) (All F, (All A, (All B, (((an_open_function_from_onto F A B) /\ ((a_continuous_function_from_onto F A B) /\ (a_locally_compact_top_space A))) => (a_locally_compact_top_space B))))) ### NotAllEx 18 % 0.18/0.40 % SZS output end Proof % 0.18/0.40 (* END-PROOF *) %------------------------------------------------------------------------------